Automatic Threshold Selection for Generalized Pareto and Pareto–Poisson Distributions in Rainfall Analysis: A Case Study Using the NOAA NCDC Daily Rainfall Database

Abstract

Both extreme-excess modeling and extreme-value analysis of precipitation events frequently utilize the Generalized Pareto (GP) distribution to model peaks above a selected threshold. However, selecting an appropriate threshold remains a complex and challenging task, which has discouraged many practitioners from employing Pareto or Pareto–Poisson distributions for extreme-value analysis. Recent analyses of threshold selection methods proposed in the technical literature, particularly when applied to rainfall records with high quantization levels, have shown that nonparametric methods are often unreliable. Additionally, methods relying on the asymptotic properties of the GP distribution tend to produce unrealistically high threshold estimates. In contrast, graphical methods and goodness-of-fit (GoF) metrics that account for the pre-asymptotic behavior of the GP distribution have demonstrated better performance. Despite these improvements, there remains no automatic and statistically robust methodology for threshold selection. This study develops an automatic, statistically sound procedure for optimal threshold selection, leveraging weighted mean square errors and internally studentized residuals. The proposed method outperforms existing approaches in terms of accuracy, as demonstrated through numerical experiments and its application to real-world data from the NOAA NCDC Daily Rainfall Database. Results indicate that the method not only improves threshold estimation precision but also enhances the reliability of extreme-value analysis for precipitation records, making it a valuable tool for hydrological applications. The findings emphasize the practical implications of the method for analyzing extreme rainfall events and its potential for broader climatological studies.